
1 Fundamental Concepts: Vectors 


1  (46) 


1  (1) 

1.2 Measure of Space and Time: Units and Dimensions 


2  (7) 


9  (6) 


15  (4) 


19  (3) 

1.6 An Example of the Cross Product: Moment of a Force 


22  (1) 


23  (2) 

1.8 Change of Coordinate System: The Transformation Matrix 


25  (5) 

1.9 Derivative of a Vector 


30  (1) 

1.10 Position Vector of a Particle: Velocity and Acceleration in Rectangular Coordinates 


31  (5) 

1.11 Velocity and Acceleration in Plane Polar Coordinates 


36  (3) 

1.12 Velocity and Acceleration in Cylindrical and Spherical Coordinates 


39  (8) 

2 Newtonian Mechanics: Rectilinear Motion of a Particle 


47  (35) 

2.1 Newton's Law of Motion: Historical Introduction 


47  (13) 

2.2 Rectilinear Motion: Uniform Acceleration Under a Constant Force 


60  (3) 

2.3 Forces that Depend on Position: The Concepts of Kinetic and Potential Energy 


63  (6) 

2.4 VelocityDependent Forces: Fluid Resistance and Terminal Velocity 


69  (6) 

2.5 Vertical Fall Through a Fluid: Numerical Solution 


75  (7) 


82  (62) 


82  (2) 

3.2 Linear Restoring Force: Harmonic Motion 


84  (9) 

3.3 Energy Considerations in Harmonic Motion 


93  (3) 

3.4 Damped Harmonic Motion 


96  (10) 


106  (7) 

3.6 Forced Harmonic Motion: Resonance 


113  (12) 

3.7 The Nonlinear Oscillator: Method of Successive Approximations 


125  (4) 

3.8 The Nonlinear Oscillator: Chaotic Motion 


129  (6) 

3.9 Nonsinusoidal Driving Force: Fourier Series 


135  (9) 

4 General Motion of a Particle in Three Dimensions 


144  (40) 

4.1 Introduction: General Principles 


144  (7) 

4.2 The Potential Energy Function in ThreeDimensional Motion: The Del Operator 


151  (5) 

4.3 Forces of the Separable Type: Projectile Motion 


156  (11) 

4.4 The Harmonic Oscillator in Two and Three Dimensions 


167  (6) 

4.5 Motion of Charged Particles in Electric and Magnetic Fields 


173  (3) 

4.6 Constrained Motion of a Particle 


176  (8) 

5 Noninertial Reference Systems 


184  (34) 

5.1 Accelerated Coordinate Systems and Inertial Forces 


184  (5) 

5.2 Rotating Coordinate Systems 


189  (7) 

5.3 Dynamics of a Particle in a Rotating Coordinate System 


196  (5) 

5.4 Effects of Earth's Rotation 


201  (6) 

5.5 Motion of a Projectile in a Rotating Cylinder 


207  (5) 

5.6 The Foucault Pendulum 


212  (6) 

6 Gravitation and Central Forces 


218  (57) 


218  (5) 

6.2 Gravitational Force between a Unifirm Sphere and a Particle 


223  (2) 

6.3 Kepler's Laws of Planetary Motion 


225  (1) 

6.4 Kepler's Second Law: Equal Areas 


226  (3) 

6.5 Kepler's First Law: The Law of Ellipses 


229  (9) 

6.6 Kepler's Third Law: The Harmonic Law 


238  (6) 

6.7 Potential Energy in a Gravitational Field: Gravitational Potential 


244  (6) 

6.8 Potential Energy in a General Central Field 


250  (1) 

6.9 Energy Equation of an Orbit in a Central Field 


251  (1) 

6.10 Orbital Energies in an InverseSquare Field 


251  (6) 

6.11 Limits of the Radial Motion: Effective Potential 


257  (3) 

6.12 Nearly Circular Orbits in Central Fields: Stability 


260  (2) 

6.13 Apsides and Apsidal Angles for Nearly Circular Orbits 


262  (2) 

6.14 Motion in an InverseSquare Repulsive Field: Scattering of Alpha Particles 


264  (11) 

7 Dynamics of Systems of Particles 


275  (48) 

7.1 Introduction: Center of Mass and Linear Momentum of a System 


275  (3) 

7.2 Angular Momentum and Kinetic Energy of a System 


278  (5) 

7.3 Motion of Two Interacting Bodies: The Reduced Mass 


283  (5) 

7.4 The Restricted ThreeBody Problem 


288  (15) 


303  (3) 

7.6 Oblique Collisions and Scattering: Comparison of Laboratory and Center of Mass Coordinates 


306  (6) 

7.7 Motion of a Body with Variable Mass: Rocket Motion 


312  (11) 

8 Mechanics of Rigid Bodies: Planar Motion 


323  (38) 

8.1 Center of Mass of a Rigid Body 


323  (5) 

8.2 Rotation of a Rigid Body about a Fixed Axis: Moment of Inertia 


328  (2) 

8.3 Calculation of the Moment of Inertia 


330  (8) 

8.4 The Physical Pendulum 


338  (6) 

8.5 The Angular Momentum of a Rigid Body in Laminar Motion 


344  (3) 

8.6 Examples of the Laminar Motion of a Rigid Body 


347  (7) 

8.7 Impulse and Collisions Involving Rigid Bodies 


354  (7) 

9 Motion of Rigid Bodies in Three Dimensions 


361  (56) 

9.1 Rotation of a Rigid Body about an Arbitrary Axis: Moments and Products of Inertia Angular Momentum and Kinetic Energy 


361  (10) 

9.2 Principal Axes of a Rigid Body 


371  (10) 

9.3 Euler's Equations of Motion of a Rigid Body 


381  (2) 

9.4 Free Rotation of a Rigid Body: Geometric Description of the Motion 


383  (1) 

9.5 Free Rotation of a Rigid Body with an Axis of Symmetry: Analytical Treatment 


384  (7) 

9.6 Description of the Rotation of a Rigid Body Relative to a Fixed Coordinate System: The Eulerian Angles 


391  (6) 


397  (4) 

9.8 The Energy Equation and Nutation 


401  (6) 


407  (2) 

9.10 Why Lance Doesn't Fall Over (Mostly) 


409  (8) 
10 Lagrangian Mechanics 

417  (48) 

10.1 Hamilton's Variational Principle: An Example 


419  (4) 

10.2 Generalized Coordinates 


423  (3) 

10.3 Calculating Kinetic and Potential Energies in Terms of Generalized Coordinates: An Example 


426  (4) 

10.4 Lagrange's Equations of Motion for Conservative Systems 


430  (1) 

10.5 Sone Applications of Lagrange's Equations 


431  (7) 

10.6 Generalized Momenta: Ignorable Coordinates 


438  (6) 

10.7 Forces of Constraint: Lagrange Multipliers 


444  (5) 

10.8 D'Alembert's Principle: Generalized Forces 


449  (6) 

10.9 The Hamiltonian Function: Hamilton's Equations 


455  (10) 
11 Dynamics of Oscillating Systems 

465  

11.1 Potential Energy and Equilibrium: Stability 


465  (4) 

11.2 Oscillation of a System with One Degree of Freedom about a Position of Stable Equilibrium 


469  (3) 

11.3 Coupled Harmonic Oscillators: Normal Coordinates 


472  (21) 

11.4 General Theory of Vibrating Systems 


493  (5) 

11.5 Vibration of a Loaded String or Linear Array of Coupled Harmonic Oscillators 


498  (7) 

11.6 Vibration of a Continuous System: The Wave Equation 


505  
Appendix A Units 

A1  
Appendix B Complex Numbers and Identities 

A4  
Appendix C Conic Sections 

A7  
Appendix D Service Expansions 

A11  
Appendix E Special Functions 

A13  
Appendix F Curvilinear Coordinates 

A15  
Appendix G Fourier Series 

A17  
Appendix H Matrices 

A19  
Appendix I Software Tools: Mathcad and Mathematica 

A24  
Answers to Selected OddNumbered Problems 

ANS1  
Selected References 

R1  
Index 

I1  